Performance analysis of digital delay lock loops in the presence of Doppler shift

The delay lock loop is a well-developed technique to track the pseudo-noise codes for spread-spectrum systems. In previous papers the first-order loop was analyzed in the absence of Doppler shift. However, under severe Doppler environment, such as low-earth-orbit (LEO) satellite communication, the tracking of PN code will be difficult for the first-order loop. This paper considers discrete time analyses of first- and second-order digital delay lock loops (DDLL), and presents the results of an investigation concerning the performance degradation due to Doppler. The performance measures evaluated include the steady-state timing error probability density function (pdf) and the mean time to lose lock. The measures are characterized in terms of the Doppler shift and the loop signal-to-noise ratio. Moreover, approximate expressions for the steady-state timing error probability density and the mean time to lose lock are also presented for the first- and second-order digital delay lock loops. The analyses are confirmed by numerical results and simulation